How to Convert a Hijri Year to Gregorian Without a Calculator

What Is the Quick Rule for Converting Hijri Years?

The rule is G = H – H/33 + 622. Here H is the Hijri year and G is the Gregorian year. It gives the Gregorian year in which the Hijri year begins, to within about one year.

A slightly more exact form is G = H × 0.970224 + 621.57. It needs a multiplication, so it is the one to use with pen and paper.

Four Steps, Shown for 1285 AH

1. Divide the Hijri year by 33. For 1285, that is 1285 ÷ 33 = 38.9.
2. Subtract the result from the year. That gives 1285 – 38.9 = 1246.1.
3. Add 622. The total is 1246.1 + 622 = 1868.1.
4. Drop the decimal for the first year and add one for the second. The answer is 1868 to 1869.

The longer form agrees. Multiply 1285 × 0.970224 to get 1246.7, then add 621.57 to reach 1868.3. Again, the range is 1868 to 1869.

Why Does the Rule Work?

It works because the Hijri year is a fixed fraction of the Gregorian year. A lunar year of twelve months is shorter, so the two counts slowly pull apart.

The Two Year Lengths

• Gregorian year: 365.2425 days on average.
• Hijri year: twelve lunar months of 29.530589 days, or 354.37 days. The 30-year tabular cycle has 10,631 days, or 354.37 days a year.

Divide one by the other and you get 0.970223. That is the 0.970224 in the longer rule.

Where the Number 33 Comes From

A Hijri year falls short by 10.88 days, which is 3.0 percent of a Gregorian year. That is one part in 33.6, close to one part in 33.

So after about 33 Hijri years, one Gregorian year has gone missing. Subtracting H/33 removes those lost years, and adding 622 puts the count back on the right starting point.

Where the Number 622 Comes From

In the tabular civil calendar, 1 Muharram of year 1 fell on Friday, 16 July 622 in the Julian calendar. That is 19 Jul 622 in the Gregorian calendar, which is day 200 of the year.

Day 200 sits at about 622.55 on the year line. Counting from year 1 instead of year 0 takes off one Hijri year. So the constant in the longer rule comes to about 621.57.

Does the Rule Match Dates From Real Sources?

Yes. The table below runs five Hijri years through the rule. Each is a year that a chronogram or a historian gives, checked against a dated source.

The sixth column is the range from the longer rule. The seventh is the span of that Hijri year in the tabular civil calendar, worked out in code. The last column is the Common Era year given by the source.

The Hijri years match the Abjad totals of lines on our how to read a chronogram and tarikh goi pages. Each total is computed by the engine and equals the stated year.

One Example in Full: 1044 AH

Divide 1044 by 33 to get 31.6. Subtract: 1044 – 31.6 = 1012.4. Add 622 to reach 1634.4.

The longer rule gives 1044 × 0.970224 = 1012.9, plus 621.57, which is 1634.5. Both say the year starts in 1634, so the range is 1634 to 1635.

A mental shortcut helps on the road. Since 33 × 30 = 990, round 1044 ÷ 33 to about 32, and 1044 – 32 + 622 = 1634.

What the Sources Say

• 1044 AH: the Wazir Khan Mosque, Lahore, is dated 1634 to 1635 by the ILCAA study of its tiles.
• 952 AH: Sher Shah Suri died on 22 May 1545 at Kalinjar. That date lies inside 952 AH in the tabular calendar.
• 1285 AH: Ghalib died on 15 February 1869. The tabular year 1285 ran from 24 Apr 1868 to 12 Apr 1869.
• 1195 AH: Frances Pritchett’s translation of Ab-e Hayat gives 1195 AH as 1780 to 1781.
• 1036 AH: Rana Safvi reports 1626 for the death of Abdur Rahim Khan-e-Khana. The tabular year 1036 began on 22 Sep 1626.

Two further dates anchor the calendar itself. The tabular epoch is 16 July 622 Julian. And 1 Muharram 1400 AH is 21 November 1979, the date in the Wikipedia article on the Islamic calendar.

How Big Is the Error?

Treat the answer as the year in which the Hijri year begins, give or take one. Both versions of the rule were tested against the tabular calendar for every Hijri year in two ranges.

The longer rule is the safer one. Its two-year range held the whole Hijri year in every case tested.

The short rule drifts. At 1445 AH it is 0.33 years behind the longer rule, because 1/33 is a little too big. Use it as a mental check, and expect the exact starting year to be wrong about one time in six.

Three Sources of Extra Error

• Calendar variant. The tests use the tabular civil calendar. Umm al-Qura and moon-sighting calendars can start a year a day or two earlier or later.
• Julian dates. Sources before 1582 give Julian dates, which run up to 10 days behind the Gregorian ones. That rarely moves a year, but it can near a boundary.
• Boundary years. When the decimal is near .00 or .99, the start of the year sits close to 1 January. A single-year answer is then close to a coin flip.

How Do You Read the Answer With No Month Known?

Give both years. For 1044 AH the rule says 1634 to 1635, and that is exactly what the mosque source states.

The figure shows why. The first 7 months of 1044 AH fall in 1634, and the last 5 fall in 1635. Without a month, you cannot say which side an event sits on.

The dates in the figure are Gregorian, even for 1634. The Julian calendar then ran about 10 days behind. A source of that period may print a date near 17 June.

Using the Month When You Have It

If a month is known, the range collapses. Find the first month of the Hijri year in the Gregorian calendar and count forward. The Hijri months page lists each month in order.

The decimal also hints at the season.

For 1285 AH the decimal is 0.31. Then 0.31 × 365 is about 113 days into 1868, which is late April.

Against the tabular calendar this hint was within about 3 days for years 900 to 1450. Still, treat it only as a month-level guide.

How Do You Convert Gregorian to Hijri?

Run the rule backward. The reverse of G = H – H/33 + 622 is H = (G – 622) × 33 ÷ 32. The reverse of the longer rule is H = (G – 621.57) ÷ 0.970224.

1. Subtract 622 from the Gregorian year. For 1869, that is 1869 – 622 = 1247.
2. Multiply by 33 and divide by 32. That gives 1247 × 33 ÷ 32 = 1285.97.
3. Round down and up. The answer is 1285 to 1286.

Ghalib’s death in February 1869 falls in 1285 AH, which sits inside that pair. The longer reverse rule gives 1285.7, which also points to 1285 and 1286.

A Gregorian year overlaps two Hijri years for the same reason. For 1634, the rule gives 1043.62, so the pair is 1043 and 1044. Both overlap 1634 in the tabular calendar.

Does the Rule Work for the Solar Hijri Year?

No. The Solar Hijri calendar, official in Iran and widely used in Afghanistan, counts solar years from the same starting event. Its years are as long as Gregorian years, so no drift builds up.

To convert a Solar Hijri year, add 621 or 622, depending on whether the Solar Hijri year has begun. Our rule is only for the lunar Hijri year, and mixing the two gives an answer about 40 years off.

Check which calendar a source uses before you convert. A year such as 1405 reads very differently as a lunar year than as a solar one.

When Should You Not Use This Rule?

Use it for orientation, such as checking that a chronogram total lands in the right century. Do not use it for a day, a weekday or a document that needs one exact date.

• For an exact date, use the chronogram decoder, which adds the letters and converts the year.
• For differences between calendar variants, see Hijri calendar systems.
• For where the era starts, see the history of the Hijri calendar.

The whole cluster is on the calendar hub. Nothing here makes any claim about the correct day for any observance.

Sources and Further Reading

• Hijri year, Wikipedia. The conversion formulas, the mean lunar year of 354.367 days, and the two-year span.
• Islamic calendar, Wikipedia. The epoch of 16 July 622 Julian, the 354.37 day year, and 1 Muharram 1400 AH.
• Tabular Islamic calendar, Wikipedia. The 30-year cycle with 11 leap years and 10,631 days.
• Deciphering the Construction Date of a Mosque Hidden in Its Mosaic Tiles, ILCAA (2025). The year 1044 AH as 1634 to 1635.
• Sher Shah Suri, Wikipedia. His death on 22 May 1545.
• Mirza Ghalib, Wikipedia. His death on 15 February 1869.
• Ab-e Hayat, chapter on Mazhar, translated by Frances W. Pritchett. 1195 AH as 1780 to 1781.
• Abdur Rahim Khan-e-Khana’s tomb in the two editions of Asar-us-Sanadid, Rana Safvi. The year 1626 and the line Khan Sipahsalar go.
• Solar Hijri calendar, Wikipedia. The 621 or 622 conversion and where the calendar is used.
• Year totals come from this site’s tested engine. See the methodology.

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